Fernandez's broadside came after the Brazilian president expressed fears Monday that a leftist victory in October elections would take Argentina on a path to economic ruin and spark an exodus.
"We don't want our Argentine brothers fleeing here," he said.
Fernandez's crushing victory over center-right President Mauricio Macri in Sunday's party primaries put him in poll position for the presidency in October's election.
And he wasted no time in hitting back at the far-right Brazilian president on Tuesday, saying in an interview on Argentine television that "I have no problems having a problem with Bolsonaro."
"I am glad Bolsonaro speaks ill of me. He is a misogynist, racist and violent."
He called on Bolsonaro to release leftist former president Luiz Inacio Lula da Silva from prison and submit to a free election contest against him.
The combative Bolsonaro -- a former army captain frequently denounced for his derogatory remarks about women and minority groups -- won Brazil's presidential election last year after overwhelming favorite Lula was barred from running and then jailed for corruption.
Neighbors Argentina and Brazil are partners -- with Uruguay and Paraguay -- in the South American economic alliance Mercosur that in June signed a huge trade pact with the European Union.
But Fernandez said he had no concerns about his ability to work with Brazil if he wins the presidency.
"We will get on splendidly with Brazil. Brazil will always be our principal partner. Bolsonaro is a mere moment in the life of Brazil, the same way Macri is a moment in the life of Argentina."
Bolsonaro on Monday said the left's return to power could put Argentina "on the same path as Venezuela," where a deepening political and economic crisis has forced millions to flee.
"If the leftists return to Argentina, we could have a new Roraima," Bolsonaro said, referring to Brazil's northern state where thousands of Venezuelans have crossed into the country.